Norwich City put in a spirited performance at Anfield before going down to a 3-1 defeat.
Forward Milot Rashica silenced Anfield three minutes into the second half with his first Premier League goal, forcing Liverpool manager Jürgen Klopp into a double change on the hour.
Liverpool then scored two goals in quick succession, from Sadio Mané and Mohamed Salah to nudge themselves in front before Luis Díaz scored his first goal for Liverpool, since his £37m transfer from Porto, to make sure of the three points.
Dean Smith made one change to the side that lost Manchester City last time out, with Mathias Normann coming in for Pierre Lees-Melou.
The Canaries started the game well with Max Aarons sending a cross that forced Allison into a save in the opening minute. Salah replied with a shot over the crossbar, but moments later Normann put Rashica in on goal and the Kosovan coolly slotted home only to be denied by offside flag.
Salah was then at the heart of the action once more, as the frantic start continued. He delivered a ball to the back post that Kostas Tsimikas should have done better with but blazed over from close range.
Liverpool continued to press for an opener as Sadio Mané sent over an inch-perfect cross for Virgil van Dijk to bring a good save out of Angus Gunn.
Norwich were a threat throughout the first half though and should have nudged in front when Brandon Williams, having a good first half against Salah, fed a pass into Teemu Pukki who fired wide from inside the box.
Luis Díaz then sent an effort over, before Salah had a shot deflect wide for a corner which he then headed towards goal forcing a Norwich defender to clear off the line.
Tsimikas then fired an effort goalwards that Gunn turned around the post. The half ended with Van Djik putting the ball into the back of the net, only for the effort to be correctly ruled out for offside, before Grant Hanley produced a superb block to deny Alex Oxlade Chamberlain.
The second half was only three minutes old when the Canaries took the lead. Josh Sargent set the goal up as he ran into the area and found Rashica whose shot deflected off Joël Matip and looped into the net.
Liverpool responded, but Hanley was there again to get a block in to deny Jordan Henderson after he was set up with a shooting chance by Salah. Further blocks denied Díaz twice, which foreced Klopp into a double change just past the hour mark bringing on Divok Origi and Thiago for Oxlade-Chamberlain and Keïta.
However, it was Mané who levelled for the hosts as Tsimikas headed a ball into the box and the Senegal international produced an acrobatic finish past Gunn.
Then three minutes later the game had been turned on its head as Allison played a long ball forward for Salah to run on to and he rolled a right-footed shot into the back of the net.
The Egyptian then went close to making it 3-1 when he picked up a cross field pass from Thiago and curled a left-foot effort just past the post. Díaz then set up Salah with another chance with 11 minutes remaining but Gunn saved well, turning his effort around the post.
However, Norwich could not withstand the pressure as Díaz secured the points with nine minutes remaining as he picked up a pass from Henderson to dink a finish over Gunn and into the bottom right hand corner.
Liverpool: Alisson; Gomez, Matip, Tsimikas; Henderson, Kieta (Origi, 60), Oxlade-Chamberlain (Thiago, 60); Mane, Salah, Diaz (Minamino, 90).
Subs not used: Kelleher, Fabinho, Konate, Milner, Robertson, Elliott.
Goals: Mane (64), Salah (67)
Norwich City: Gunn; Aarons, Gibson, Hanley (C), Williams; Normann (Lees-Melou, 82), Gilmour, McLean; Sargent (Płacheta, 76), Pukki, Rashica (Rowe, 86).
Subs not used: McGovern, Byram, Zimmermann, Dowell, Kabak, Lees-Melou, Giannoulis.
Goals: Rashica (48)**\
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Bookings:** Williams (40)
Referee: Mike Dean
HT: 0-0
Venue: Anfield
Attendance: TBC